Pre-service Elementary Mathematics Teachers’ Planning Processes of Mathematical Modeling Practices

Öz

In this study, it was aimed to examine the changes in the course planning processes of six pre-service elementary mathematics teachers with mathematical modeling problems in the teaching dimension of mathematical modeling teaching competencies during the lesson study. The research, which is a qualitative case study, was conducted in two dimensions: theoretical education and practice. Pre-service teachers who received theoretical training on mathematical modeling prepared implementation plans for two different mathematical modeling problems and implemented these plans in the classroom environment. The data obtained from the planning processes were analyzed using qualitative data analysis methods. The findings showed that the lesson study model made significant contributions to the lesson planning processes of pre-service teachers with modeling problems. It was seen that the pre-service teachers have gone through detailed planning processes and that there were similarities as well as significant differences in their plans.

Anahtar Kelimeler

• Lesson study
• mathematical modeling
• teaching competencies
• pre-service teachers
• planning

Ortaokul Matematik Öğretmen Adaylarının Matematiksel Modelleme Uygulamalarını Planlama Süreçleri

Öz

Bu çalışmada, ortaokul matematik öğretmen adaylarının ders imecesi boyunca matematiksel modelleme öğretiminde öğretmen yeterliklerinden biri olan öğretme boyutunda yer alan matematiksel modelleme problemleriyle uygulamayı planlama süreçlerindeki değişimin incelenmesi amaçlanmıştır. Nitel bir durum çalışması olan araştırma, teorik eğitim ve uygulama olmak üzere iki boyutta gerçekleştirilmiştir. Matematiksel modelleme ile ilgili teorik eğitim alan öğretmen adayları iki farklı matematiksel modelleme problemi için uygulama planı hazırlamış ve bu planlarını sınıf ortamında hayata geçirmişlerdir. Planlama süreçlerinden elde edilen veriler nitel veri analiz yöntemleri kullanılarak analiz edilmiştir. Elde edilen bulgular, ders imecesi modelinin, öğretmen adaylarının matematiksel modelleme problemleriyle uygulama planlama süreçlerine önemli katkılarının olduğunu göstermiştir. Öğretmen adaylarının ayrıntılı planlama süreçlerinden geçtikleri ve planlarında benzerliklerin yanı sıra önemli farklılıkların olduğu görülmüştür.

Anahtar Kelimeler

• Ders imecesi
• matematiksel modelleme uygulamaları
• planlama
• öğretim yeterlikleri
• öğretmen adayları

Kaynakça

1. Alhammouri, A. M. (2018). Professional development in mathematical modeling: Teacher engagement, teacher knowledge, and classroom implementation (Unpublished doctoral dissertation). Ohio, Ohio University.
2. Ang, K. C. (2015). Mathematical modelling in Singapore schools: A framework for instruction. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 57–72). Singapore: World Scientific. doi:10.1142/9789814546928_0004
3. Blum, W. (2015, July 8-15). Quality teaching of mathematical modelling: What do we know, what can we do? [Conference session]. The Proceedings of the 12th International Congress on Mathematical Education, Seoul, Korea.
4. Blum, W., & Borromeo Ferri, B. R. (2009). Mathematical modeling: Can it be taught and learnt?. Journal of Mathematical Modeling and Aplications, 1(1), 45-58.
5. Borromeo Ferri, R. (2007, February 22-26). Personal experiences and extra-mathematical knowledge as an influence factor on modelling routes of pupils [Conference session]. Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, Larnaca, Cyprus.
6. Borromeo Ferri, R. (2010). On the Influence of Mathematical Thinking Styles on Learners’ Modeling Behaviour. Journal für Mathematik-Didaktik, 31(1), 99-118. doi: 10.1007/s13138-010-0009-8
7. Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer.
8. Borromeo Ferri, R., & Blum,W. (2009, January 28-February 1). Mathematical modelling in teacher education experiences from a modelling seminar [Conference session]. Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, Lyon, France.

9. Bukova Güzel, E. (Editör). (2016). Matematik eğitiminde matematiksel modelleme. Pegem Akademi.
10. Cai, J., Cirillo, M., Borromeo Ferri , R., & Geiger, V. (2014, July 15- 20). Mathematical modeling in school education: Mathematical, cognitive, curricular, instruciıonal and teacher education perspectives [Conference session]. Proceedings of the joint meeting of PME 38 and PME-NA 36, Vancouver, Canada.
11. Common Core State Standards Initiative [CCSSM]. (2010). Common core state standards for mathematics. https://learning.ccsso.org/common-core-state-standards-initiative adresinden 30 Mayıs 2023 tarihinde alındı.
12. Cakmak Gurel, Z., & Bekdemir, M. (2022). The Teacher and Peer Intervention for Pre-service Mathematics Teachers on the Validity of Mathematical Models. Pedagogical Research, 7(2), em0120. doi:10.29333/pr/11800
13. Creswell, J. W. (2016). Nitel araştırma yöntemleri (Çev. M. Bütün ve S. B. Demir). Siyasal Yayınları.
14. Didiş Kabar, G., & İnan Tutkun, M. (2021). Investigating Middle School Mathematics Teachers’ Implementation Process of a Mathematical Modelling Problem: Planning of Implementation and Teacher Interventions. International Journal of Educational Studies in Mathematics, 8(2), 98-123. doi:/10.17278/ijesim.878364
15. English, L. D., & Watters, J. J. (2005). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 58–79.
16. Eraslan, A. (2008). Japanese lesson study: Can it work in Turkey?. Education and Science, 33 (149), 62-67.
17. Erbaş, A. K., Çetinkaya, B., Alacacı, C., Çakıroğlu, E., Aydoğan Yenmez, A., Şen Zeytun, A., Korkmaz, H, Kertil, M., Didiş, M. G., Baş, S., & Şahin, Z. (2016). Lise matematik konuları için günlük hayattan modelleme soruları. Türkiye Bilimler Akademisi.
18. Erbaş, A. K., Çetinkaya, B., & Çakıroğlu, E. (2013). Ortaöğretim matematik eğitiminde matematiksel modelleme: Hizmetiçi ve hizmetöncesi öğretmen eğitimi (TÜBİTAK Proje No: 110K250). Yayınlanmamış rapor, TÜBİTAK.
19. Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modellin and Applications. 1(5), 3-16.
20. Henn, H. W. (2007). Modelling pedagogy - overview. In W. Blum, P. L. Galbraith, H. W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 321–324). New York: Springer. doi:10.1007/978-0-387-29822-1_33
21. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
22. Leiß, D., & Wiegand, B. (2005). A classification of teacher interventions in mathematics teaching. ZDM, 37(3), 240-245.
23. Lewis, C. (2009). What is the Nature of Knowledge Development in Lesson Study?. Educational Action Research,17(1), 95-110. doi: 10.1080/09650790802667477
24. Lewis, C., & Tsuchida, I. (1998). A Lesson is Like a Swiftly Flowing River: How Research Lessons Improve the Japanese Education. Improving Schools, 2(1), 48-56. doi: 10.1177/136548029900200117
25. Maaß, K., & Gurlitt, J. (2009). Designing a teacher questionnaire to evaluate professional development in modelling. In V. Durand Guerrier, S. Soury Lavergne & F. Arzarello (Eds.), Proceedings of CERME 6 (pp. 2056–2065). France: Institut national de recherche pédagogique.
26. Milli Eğitim Bakanlığı [MEB], (2005). Ortaöğretim matematik (9-12. Sınıflar) dersi öğretim programı. Talim ve Terbiye Kurulu Başkanlığı.
27. Milli Eğitim Bakanlığı [MEB], (2013). Ortaöğretim matematik (9-12. Sınıflar) dersi öğretim programı. Talim ve Terbiye Kurulu Başkanlığı.
28. Murata, A. (2011). Intruduction. conceptual overview of lesson study. In L, C, Hart, A. Alston & A. Murata (Eds.), Lesson study research and practice in mathematics education (pp. 1-12). Springer.
29. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
30. Sağıroğlu, D., & Karataş, İ. (2018). Matematik Öğretmenlerinin Matematiksel Modelleme Yöntemine Yönelik Etkinlik Oluşturma ve Uygulama Süreçlerinin İncelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 12(2), 102-135. doi:10.17522/balikesirnef.506423
31. Stender, P., & Kaiser, G. (2015). Scaffolding in Complex Modelling Situations. ZDM, 47(7), 1255-1267. doi: 10.1007/s11858-015-0741-0
32. Tekin Dede, A., & Bukova Güzel, E. (2023a). Developing a Framework to Support Teachers’ Implementation of Mathematical Modelling, International Journal of Mathematical Education in Science and Technology. doi:10.1080/0020739X.2023.2204098
33. Tekin Dede, A., & Bukova Guzel, E. (2023b). Reflections from Planning and Implementing a Modelling Task. International Electronic Journal of Mathematics Education, 18(1), em0728. doi:10.29333/iejme/12821
34. Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri (Çev. M. Bütün & S. B. Demir). Pegem Akademi.
35. Tropper, N., Leiss, D., & Hänze, M. (2015). Teachers’ Temporary Support and Worked-out Examples as Elements of Scaffolding in Mathematical Modeling. ZDM, 47(7), 1225-1240. doi: 10.1007/s11858-015-0718-z
36. Wess, R., Klock, H., Siller, H. S., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical Modelling Education in East and West (pp. 249–260). Cham: Springer International Publishing. https://doi. org/10.1007/978-3-030-66996-6_21
37. Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Seçkin Yayıncılık.